This invention relates generally to tessellatable elements and more specifically, but not exclusively, to tessellations for covering surfaces.
The covering of surfaces such as floors, walls and ceilings with decorative patterns is well known. Often, floor surfaces are covered with bricks, paving stones or other such similar media. One way decorative patterns can be made is to periodically repeat shapes to build-up a mosaic-like covering. These types of patterns will often have an inherent symmetry; translational, rotational, etc.
Decorative patterns can be realised using such tessellatable elements as are disclosed in U.S. Pat. No. 5,945,181. Here, heptagonal and pentagonal elements are tessellated to produce patterns and/or decorations suitable for covering floor or walls.
Certain surface spaces cannot be tiled totally with heptagonal and/or pentagonal tiles only, since gaps will result if rectangular spaces are tiled with such elements. The only remedy to this problem would be to cut the tiles to achieve `wall-to-wall` coverage. The aesthetic nature of designs made with such tiles is also limited.
The present invention arose in an attempt to provide a set of elements capable of tessellating a surface which is delimited by straight perimeter edges or otherwise, without having to pre-cut any of the elements.
It was also desirable to minimise the number of different shaped elements within a given set, and also to devise sets whose elements could be interchanged.
A further object of the invention is to provide a set of elements which can be tessellated in many different ways, to produce very attractive patterns.